Harry is not Gryffindor's heir (was Horcruxes: Groundrules and Theories

[fanofminerva]

No: HPFGUIDX 136430

--- In HPforGrownups at yahoogroups.com, Morgan Adams 
<MorganAnnAdams at y...> wrote:
> 
> ongj87 wrote: "I think, putting the rivalry of Slytherin and 
Gryffindor together with the prophecy, he concluded that the one to 
be his equal and rival would obviously be the heir to Gryffindor."
> 
> Morgan here: JKR has shot down that theory. Read the text of her 
Leaky Cauldron/Mugglenet interview below where she states that Harry 
is not the hair of Gryffindor:
> 
> MA: What about Harry's family — his grandparents — were they 
killed?
> 
> JKR: No. This takes us into more mundane territory. As a writer, 
it was more interesting, plot-wise, if Harry was completely alone. 
So I rather ruthlessly disposed of his entire family apart from Aunt 
Petunia. I mean, James and Lily are massively important to the plot, 
of course, but the grandparents? No. And, because I do like my 
backstory: Petunia and Lily's parents, normal Muggle death. James's 
parents were elderly, were getting on a little when he was born, 
which explains the only child, very pampered, had-him-late-in-life-
so-he's-an-extra-treasure, as often happens, I think. They were old 
in wizarding terms, and they died. They succumbed to a wizarding 
illness. That's as far as it goes. There's nothing serious or 
sinister about those deaths. I just needed them out of the way so I 
killed them.
> 
> MA: That sort of shuts down Heir of Gryffindor [theories], as well.
> 
> JKR: [Pause.] Yeah. Well - yeah. 
> 
> MA: Another one bites the dust.
> 
> --Morgan
> 
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I read that in the interview and again in this post.  However, I 
need help with something.  Just how DOES this shoot down the heir of 
Gryffindor theories?  How does JKR's answer/backstory answer this?  
I was confused by MA's follow-up question then and I still am.  
Please enlighten!